Resolutions of moduli spaces and homological stability

Details Resolutions of moduli spaces and homological stability Resolutions of moduli spaces and homological stability

2009-09-23

arxiv.org/abs/0909.4278v3

Mathematics

Algebraic Topology

53 pages, 8 figures; V2: Warning, Completely Revised Version; V3: Removed discussion of configuration spaces

Scientific paper

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.

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